1. Technical Field
The present disclosure relates generally to acquisition of imaging signal and reconstruction of images from the acquired signals, and more particularly to acquisition and reconstruction of images using compressed sensing techniques.
2. Discussion of Related Art
Magnetic resonance imaging (MRI) is a non-invasive diagnostic imaging procedure that uses nuclear magnetization and radio waves to produce internal images of a patient. An MRI scanner contains magnetic coils that create a strong static magnetic field in which the patient is positioned. Certain atoms in a patient's body that were previously randomly-ordered become aligned along the magnetic field. The scanner then sends a series of bursts or pulses of radio frequency (RF) energy through the patient's body part under examination that excite the “ordered” atoms to specific oscillations around the magnetic field. The atoms generate an RF signal during the pulsed oscillations and as the atoms return to their respective alignments. The scanner detects the RF signals by appropriate reception or pick-up coils and uses gradient coils to generate non-homogeneous magnetic fields to enable the signals to be spatially coded in all three spatial directions. The scanner processes the coded signals or data to transform them into a visual representation of the scanned patient's body part. In particular, the scanner samples and digitizes the signals, creates a so-called k-space data matrix filled with the digitized complex values of each signal, and generates for display and/or other usage a corresponding MR image from the k-space data matrix by means of a complex Fourier transform. The MRI scanner acquires three-dimensional image data of the patient's body part for respective “slices” of an area of the body part. The scanner repeats a pre-defined MR image pulse sequence, i.e., the above-described steps for collecting the signals/data, a number of times to collect sufficient data from the excitations to reconstruct the specific image. Ideally, there are little or no variations in the nuclear magnetization during the excitations.
Image acquisition may be performed under time-sensitive conditions to ensure that there is no movement of the subject during the image acquisition process. Thus, image acquisition may be performed while the patient refrains from moving. Often this is requires the patient holding his breath. When the MRI is used to track cardiac motion, acquisition time needs to be quick.
In light of this shortened acquisition time, it may be difficult to acquire data at the Nyquist rate to ensure sufficient sampling for ideal image reconstruction. Accordingly, performing accurate reconstruction with less than an ideal amount of data may be difficult. This difficulty in reconstructing an image under these conditions may be similar to trying to solve for a system of linear equations in which there are more unknown variables then there are equations. In such a case, there may be an infinite number of possible solutions.
Compressed sensing (CS) techniques have been developed to aid in reconstructing a signal using a sampling rate that is below the Nyquist sampling rate. These techniques exploit the observation that most practical signals of interest have sparse representations using a specific transform. Thus, for a given signal, there may exist a particular transform space in which a majority of the transform coefficients are at or near zero. This transform space may be referred to as the sparsity space. As these small coefficients may be assumed to be zero without significant loss of signal quality (the sparseness assumption), signal reconstruction may be approximated by determining only the limited set of large transform coefficients for the sparsity space.
In standard MRI acquisition, oversampling may be performed along a frequency encoding (or readout) direction to avoid aliasing (or wrapping) artifacts. In radial trajectory acquisition, the oversampling may be performed in each “readout” direction of radial spokes. This oversampling is usually not an issue for a modern scanner and does not increase the total reconstruction time. However, for CS reconstruction, it is quite time-costly due to non-linear iterative optimization involved to process the extra oversampled data. The time spent on reconstructing the peripheral background is considered time wasted since in most cases they are zeros or close to zero (e.g., background noise), and will be thrown away at the end of reconstruction.
Thus, there is a need for methods and systems that can improve CS reconstruction.